A laser cavity will support multiple modes in its cavity, all you need is to have the round trip be an integral number of wavelengths. The modes will be separated by the free spectral range of the cavity, at slightly different frequencies.

So a laser that is single longitudinal mode is lasing in only one of those modes, i.e. at a single frequency. Saying the laser is single-mode also tends to imply that the laser is not hopping between modes (i.e. single mode at any given time, but multiple modes present over a large amount of time.)

The modes will be separated by the free spectral range of the cavity, at slightly different frequencies.

So a laser that is single longitudinal mode is lasing in only one of those modes, i.e. at a single frequency. Saying the laser is single-mode also tends to imply that the laser is not hopping between modes (i.e. single mode at any given time, but multiple modes present over a large amount of time.)

What exactly is the free spectral range of the cavity? And do mode hops have anything to do with the energy gap that electrons move across when they emit photons?

The FSR of a cavity is defined as the maximum range of frequencies that the cavity can resolve. The term FSR is borrowed from laser physicists to describe the longitudinal mode separation, however often the FSR does not equal the longitudinal mode separation because of intra or extra cavity elements on the active medium itself.

Lots of things can cause mode hops, slight changes in the laser cavity (such as thermal expansion), or external feedback are two things that commonly cause mode hops in lasers.

The FSR of a cavity is defined as the maximum range of frequencies that the cavity can resolve. The term FSR is borrowed from laser physicists to describe the longitudinal mode separation, however often the FSR does not equal the longitudinal mode separation because of intra or extra cavity elements on the active medium itself.

Lots of things can cause mode hops, slight changes in the laser cavity (such as thermal expansion), or external feedback are two things that commonly cause mode hops in lasers.

Claude.

So if I understand correctly, would the FSR be dependent on the number of integer wavelengths you can have within the laser cavity? And would this be in relation to internal or external cavities?

Also, do you know of any literature that might be useful to fully understand the theory behind mode hops?

The FSR is defined by the spacing of the mirrors, and the refractive index of the medium within the cavity (sometimes termed the optical path length).

The term FSR can be applied to any cavity as far as I know.

Most literature would be in relation to Semiconductor Lasers where mode hopping is more prevalant and difficult to control, though most introductory laser textbooks will provide a brief insight as to why mode hopping occurs.

I have a better idea of what mode hopping is now and I have come across some material that says the different modes that you can get for a laser diode are represented by a series of peaks under a so called 'gain profile' and that the wavelength at which the laser will operate corresponds to the peak that is closest to the maximum value of the 'gain profile'.

I am slightly confused about the meaning of the 'gain profile'. Is it anything to do with the einstein's A and B coefficients or am I totally off track? Maybe you can shine some light onto this!

The gain profile of a laser depicts the gain of the medium as a function of frequency, and is useful in characterising the active medium, without relying on cavity parameters. Gain profiles are usually found through experiment, rather than from theoretical principles, though almost all laser phenomena can be related in some way to Einstein's A and B coefficients.